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Constant term - fixed effects

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Dear all,

This might be a silly question, however, can't find any information about it online (there is a lot on the constant term but little when dealing with its significance). I understand that the constant of the fixed effects regression (-xtreg, fe-) is the average value of the fixed effects across the entities. I have a non-significant constant coefficient - i.e. the average fixed effects are not significantly different from zero. Does this imply that the fixed effects model is not to be preferred? Or is it simply that the fixed effects, on average, is low such that it is insignificant thus a fixed effects model would still be appropriate?

Thank you in advance!

Best,
Magnus

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